7. Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. ### Understanding the Standard Normal Distribution CurveThe image above illustrates a standard normal distribution curve, which is a common way to visualize probabilities of a normally distributed variable. This distribution is defined by its bell-shaped curve, symmetrical around the mean (typically set at 0 when standardized).#### Key Elements Shown in the Diagram:1. **Bell Curve**: The blue curve represents the standard normal distribution, which is symmetrical and unimodal. The highest point on the curve occurs at the mean, µ = 0, and the curve diminishes towards the extremes.2. **Shaded Area**: The area under the curve that is shaded in blue indicates the probability of a random variable falling within a specific range of values. This shaded region spans from z = -0.95 to z = 1.26. 3. **Z-Scores**: - **z = -0.95**: This is one boundary of the shaded region on the left side of the mean. - **z = 1.26**: This is the other boundary of the shaded region on the right side of the mean. #### Interpretation of the Graph:- The **z-score** is a measure that describes a value's relationship to the mean of a group of values. By definition, the mean of the standard normal distribution is 0, and its standard deviation is 1.- The **area under the curve** between any two z-scores represents the probability of a random variable falling within that range.- The probabilities that correspond to these z-scores help determine outcomes in various fields such as statistics, finance, research, and more. #### Practical Application:Understanding z-scores and the areas under the standard normal distribution curve can help statistically determine the likelihood of events. For instance, if you want to know the probability that a randomly selected data point falls between z = -0.95 and z = 1.26, you would look at the shaded area under the curve between these points.This visualization assists in making decisions based on probabilistic outcomes, contributing significantly to more accurate analyses and predictions in research and various applied fields.

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Answered: 7. Find the area of the shaded region.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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7. Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

### Understanding the Standard Normal Distribution Curve

The image above illustrates a standard normal distribution curve, which is a common way to visualize probabilities of a normally distributed variable. This distribution is defined by its bell-shaped curve, symmetrical around the mean (typically set at 0 when standardized).

#### Key Elements Shown in the Diagram:

1. **Bell Curve**: The blue curve represents the standard normal distribution, which is symmetrical and unimodal. The highest point on the curve occurs at the mean, µ = 0, and the curve diminishes towards the extremes.

2. **Shaded Area**: The area under the curve that is shaded in blue indicates the probability of a random variable falling within a specific range of values. This shaded region spans from z = -0.95 to z = 1.26.

3. **Z-Scores**:
- **z = -0.95**: This is one boundary of the shaded region on the left side of the mean.
- **z = 1.26**: This is the other boundary of the shaded region on the right side of the mean.

#### Interpretation of the Graph:

- The **z-score** is a measure that describes a value's relationship to the mean of a group of values. By definition, the mean of the standard normal distribution is 0, and its standard deviation is 1.
- The **area under the curve** between any two z-scores represents the probability of a random variable falling within that range.
- The probabilities that correspond to these z-scores help determine outcomes in various fields such as statistics, finance, research, and more.

#### Practical Application:

Understanding z-scores and the areas under the standard normal distribution curve can help statistically determine the likelihood of events. For instance, if you want to know the probability that a randomly selected data point falls between z = -0.95 and z = 1.26, you would look at the shaded area under the curve between these points.

This visualization assists in making decisions based on probabilistic outcomes, contributing significantly to more accurate analyses and predictions in research and various applied fields.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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